for all \((z, z^{\prime })\in X\times X\)  and \(f\)  is injective.
See for instance [1]} for the proof for planar domains. The cases for Riemann surface can be proved similarly. A consequence of the property is the following rigidity property Lemma REF  of the Green's function. We note that strengthened forms of the subordination property and Lemma REF  were proved in [2]} by Minda using the Lindelöf principle for the Green's function.
